Can we really say goodbye to the cold war while holding on to Trident? Photograph: Lt. Stuart Antrobus/EPA

It's hard to think of anything more symbolic of the cold war than nuclear weapons. So it was more than a touch bizarre to hear from defence secretary Liam Fox that "we need to say goodbye to the cold war" in the imminent strategic defence review, but that Trident will be excluded from consideration.

While Dr Fox promises a root-and-branch rethink in all other military areas, he has chosen to exempt the unused and unusable weapon that senior military figures have described as "completely useless". When there are so many other calls on funding for the forces' needs – never mind any other public spending – it seems like a dereliction of duty not even to consider non-replacement. After all, the Tories presumably don't have the same hang-ups about appearing weak on defence, which often seem to inhibit the Labour leadership in this area.

Meanwhile, other developments were afoot that made me wonder anew if government departments inhabit parallel universes. Foreign secretary William Hague – almost simultaneous with Fox's speech – made a ministerial announcement on the recent nuclear non-proliferation treaty review conference. He was "delighted" that the conference had successfully reached agreement "to pursue the goal of a world without nuclear weapons". The UK, following Clinton's lead for the US, had announced the size of its warhead stockpile – 225 – in a bid to increase transparency and trust. A small step, but not an irrelevant one, in the global context. The UK also strongly backed a WMD-free zone in the Middle East, and has committed to re-examining its nuclear declaratory policy – when we will use them – as part of a wider process of reducing the significance of nuclear weapons in military postures worldwide.

So how do these seemingly contradictory policies – rearmament and disarmament – coexist? Oddly, the government thinks they are fully compatible – a position that the Labour government also held. So we continue in an Alice in Wonderland world where you get new nukes in order to demonstrate your commitment to disarmament.

It is hard to see how the Liberal Democrats fit into this illogical jigsaw. They had an eminently sensible election policy of including Trident in the defence review and considering all options, up to and including non-replacement. That has clearly fallen victim to the coalition agreement. But it is to be hoped that they will at least take up their promised concession of scrutinising the cost-effectiveness of Trident and continuing to argue for alternatives. I look forward to finding out how and when that process will take place.